Math

QuestionFind the factored form of 3x3+15x218x3x^{3} + 15x^{2} - 18x.

Studdy Solution

STEP 1

Assumptions1. The given expression is 3x3+15x18x3 x^{3}+15 x^{}-18 x . We need to factorize this expression

STEP 2

First, we observe that each term in the expression has a common factor of xx. We can factor out this common factor.
x+15x218x=x(x2+5x6) x^{}+15 x^{2}-18 x =x(x^{2}+5x-6)

STEP 3

Now, we need to factorize the quadratic expression x2+5x6x^{2}+5x-6. This can be done by finding two numbers that multiply to -6 (the constant term) and add to5 (the coefficient of xx).

STEP 4

The two numbers that satisfy these conditions are6 and -1. Therefore, we can write x2+x6x^{2}+x-6 as (x1)(x+6)(x-1)(x+6).

STEP 5

Substitute (x1)(x+)(x-1)(x+) back into the factored expression from2.
3x(x2+5x)=3x(x1)(x+)3x(x^{2}+5x-) =3x(x-1)(x+)So, the factored form of 3x3+15x218x3 x^{3}+15 x^{2}-18 x is 3x(x1)(x+)3x(x-1)(x+).

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